$L^2$-Alexander torsion and higher-order torsion degree conjecture

Let $K$ be an oriented knot, let $\pi_K$ denote its knot group, and let $\gamma\colon\pi_K\to\Gamma$ be an epimorphism onto a nontrivial torsion-free elementary-amenable group. $L^2$-higher-order degree conjecture. Then

$$\deg\left(\tau^{(2)}(K,\gamma)(t)\right)=\deg\left(\tau(K,\gamma)\right).$$

The conjecture proposes that $L^2$-Alexander torsions generalize higher-order Alexander torsions by preserving their degree. The source does not report a resolution.